Computational mechanics emphasizes the development of mathematical models representing physical phenomena including the application of modern computing methods to analyze these phenomena. It draws on the disciplines of physics, mechanics, mathematics and computer science, and encompasses numerical methods for application to various civil engineering problems. Strong teaching and research ties exist between the program and the Division of Mechanics and Computation of the Mechanical Engineering Department. Collaborative research with the Scientific Computing and Computational Mathematics Program in the Department of Computer Science in high-performance computing, emphasizing the development of finite element solution methods for structural analysis on massively parallel computers, is also well established. Numerous application areas are being investigated including constitutive modeling for structural and geomaterials, advanced computational methods for structural dynamics problems, soil-structure interaction, and simulation of semiconductor devices.

Work in computational mechanics is concerned with developing numerical modeling and solution procedures for a broad variety of physical problems in structural and geotechnical analysis. The general scope of this work includes fundamental studies of the accuracy, stability, and efficiency of finite element methods and finite difference techniques, as well as the development of new classes of methods. This work is important not only for its utility in analysis and design, but also because it can develop valuable tools for studying the fundamental mechanisms of complex and often nonlinear phenomena important in many engineering problems.

Some examples of research presently being undertaken in computational mechanics include the development of new stabilized finite element methods for transient dynamic analysis of fluid-soil-structure systems, mathematical formulation and modeling of high-gradient problems in solid mechanics, application of elastic and inelastic fracture mechanics to steel structures, modeling of large deformation and instability in inelastic materials, and multiscale modeling via the finite element method. Research being undertaken in the area of structural mechanics includes the development of constitutive models for new high performance materials such as ductile fiber-reinforced concrete, modeling of time-dependent response including durability of advanced fiber-reinforced composites, and modeling of nonlinear response of structural systems that use high performance composite materials. Emphasis is placed on developing models that are based on micro-structural behavior and can be applied efficiently to large-scale infrastructure simulations. In computational plasticity, various numerical integration algorithms are currently being developed for application to complex plasticity models such as those encountered in geomechanics. Specific problems of interest include damage and strain localization in metals, concrete, soils, and rocks, and liquefaction instability in saturated granular materials.

Our group is actively involved in interdisciplinary research bridging departments such as Mechanical Engineering, Computer Science, Electrical Engineering, Materials Science and Engineering, and Geological and Environmental Sciences.

Parallel and Distributed Computing

In order for a computational technique to be competitive, it is essential to consider not only the discretization procedure (e.g. finite elements), but also how the equations will be solved. While it is generally acknowledged that parallel supercomputing offers considerable promise for solving very large problems of practical interest, it is important to recognize that new algorithms and data structures have to be developed to exploit the new discretization methods and also to attack the intrinsic difficulties of the physical problem being addressed. Adaptive solution schemes based on error estimation also provide unique challenges for solver technology. Current work in our group related to parallel and distributed computing involves the development of new solution algorithms for statics and dynamics problems. It is expected that research in this area will continue to grow, as evidenced by the explosion of new parallel computers, and networked workstations available in the last few years. Philosophically, the objective of research in this area is to reexamine traditional ways of thinking about computational mechanics and to express the problems using new and non-classical concepts and strategies that will enable full utilization of state of the art computer technology.

AI and Data Base Applications

We view this research area as a solution to problems usually faced by engineers when dealing with very sophisticated analysis codes, and involves the development of an intelligent front-end interface that can guide the engineer to properly model the problem and select the appropriate type of analysis procedure using applications which can easily be understood. This computational mechanics issue is design-oriented and can be suitably integrated in the form of geometric modeling, database management, CAD, knowledge-based pre- and post-processors, and adaptive methods.